弦振动定解问题级数解的截断误差分析

教学研究

弦振动定解问题级数解的截断误差分析

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韩社教( 1966—) ，男，陕西武功人，西安电子科技大学物理与光电工程学院教授，博士，主要从事电磁

收稿日期: 2018-04-16

修回日期: 2018-05-27

网络出版日期: 2019-02-27

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Analysis of the truncation error of series solutions for vibrating string problem

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1.School of Physics and Optoelectronic Engineering，Xidian University，Xi'an，Shaanxi 710071，China; 2.School of Aerospace and Technology，Xidian University，Xi'an，Shaanxi 710071，China

Received date: 2018-04-16

Revised date: 2018-05-27

Online published: 2019-02-27

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基于弦振动方程在定解条件下的三种不同形式的级数解，讨论了是否忽略自变量两种条件下级数解的截断误差.其中，在考虑自变量的情况下通过对普遍截断误差进行估计，定义出类吉布斯现象，从而得到最大截断误差的估计.

关键词： 弦振动方程; 截断误差; 类吉布斯现象

韩社教, 何家奇 . 弦振动定解问题级数解的截断误差分析[J]. 大学物理, 2019 , 38(1) : 8 . DOI: 10.16854 /j.cnki.1000-0712.180241

Based on three different forms of the series solutions of the vibrating string equation under the definite

condition，the truncation error of the series solutions is discussed in two different conditions，ignoring or not ignoring

the independent variables. When the independent variables，by estimating the general truncation error，defining

the Gibbs-like phenomenon is considered，we obtain the estimation of the maximum value of the truncation error.

Key words： vibrating string equation; truncation error; Gibbs-like phenomenon

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